Find areas and perimeters of composite rectilinear figures

What you will learn

• Find areas and perimeters of composite rectilinear figures

Models used: number sentences, stories, diagrams.

Before you start

• Find missing rectangle or square dimensions from area or perimeter

Split the shape into familiar pieces

Imagine the full 6 by 4 rectangle. It would cover 24 square units.

1. Imagine the full 6 by 4 rectangle. It would cover 24 square units.

2. A 2 by 2 corner is missing. That missing square covers 4 square units.

3. Only count the area that is still there: 24 minus 4 is 20.

   6 × 4 − 2 × 2 = 20

Worked example: A new example, together

A 5 cm by 6 cm rectangle has a 1 cm square corner removed. Find the area of the remaining L-shape.

1. Identify the surface to cover and the lengths that determine its rows. Keep missing or overlapping pieces visible.

   Area counts the surface covered by square units, with missing parts removed.

2. The full rectangle covers 5 × 6 = 30 square centimetres.

   A 5 cm by 6 cm rectangle has a 1 cm square corner removed. Find the area of the remaining L-shape.

   29 cm²

3. The missing square covers 1 × 1 = 1 cm².

4. 30 − 1 = 29 cm².

5. Check the result against the question we started with.

   29 + 1 = 30.

   We found 29 cm². Area counts the surface covered by square units, with missing parts removed.

Common mistakes to discuss

• Using the outside measurements only. Split the figure into parts, find each part, then combine. A missing side is found from the sides facing it.

Check your understanding

• Find areas and perimeters of composite rectilinear figures
• explain area calculations using covered square units
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.